Stability and stabilization for nonlinear discrete-time singular Markov jump systems with time-varying delay

In this paper, stability and state feedback stabilization for nonlinear discrete-time singular Markov jump systems with time-varying delay is discussed. Based on Lyapunov theory and the implicit function theorem, a linear matrix inequality (LMI) sufficient condition is developed which guarantees that the nonlinear discrete-time singular Markov jump systems with time-varying delay are regular, causal, have unique solution in a neighborhood of the equilibrium point, and are stochastically stable. Then, in order to facilitate the design of the controller, based on this stability condition, by using a series of matrix inequalities, another LMI stability condition is obtained, and the design method of state feedback controllers is given. Last, a numerical example is given to show the effectiveness and correctness of the proposed method.